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I have heard that a minimum frequency (Threshold frequency) is required for photoelectric effect to take place, and photoelectric current is independent of frequency of incident light. That means after threshold frequency is reached, photoelectric current would be observed, and further increase in frequency won't effect the current. However, one of my textbooks show this plot.

enter image description here

How does photoelectric current increases when frequency increases after $\nu_o$?

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The classical way of calculating parameters for the photoelectric effect use the following variable for the y axis, not current:

enter image description here

The variable is "maximum photoelectron kinetic energy", which allows for an easy interpretation, and the need for quantization.

Look at the definition of the current in terms of electrons, the velocity of the electron is proportional to the current.

As energy of the incoming photon is $E=hν$, the higher the frequency the more energy is transferred to the kicked electron, the higher its velocity, and that is what the curve shows

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